It is called the early edge program. I think you're eligible after a year. You have to trade in your old phone to qualify and that gets you out of your contract and eligible to upgrade.
I wasn't on the edge program. To be eligible to edge up you have to have already been on the edge program. Besides, I just got my 5s in May. So it has only been 5-6 months so far
The way it is advertised after you are done with your 2 year contract. You can choose between edge or another contract. If you are still in the contract then it won't let you. And on the vz website in the portion that is information about edge. One of the faq's is who is eligible for edge. And it says that your device must be eligible for an upgrade. My phone was not at all eligible. The website said I would be eligible like 5/31/16